Safari 12.0 on my 2017 iMac cannot resolve local computer names. In my particular case the computer is a RaspberryPi with a default web page.
If I put "pi-star.local" in the Safari address box, I receive "Safari can't open the page pi-star.local because the server unexpectedly dropped the connection". Safari loads the webpage if I put in the ip address instead.
pi-star.local works fine in Chrome and Firefox and webpage loads. I can also ping pi-star.local in terminal.
I have checked the Discovery App (for Bonjour from the Mac App Store) and can see pi-star.local listed.